ON THE AUTOMORPHISM GROUP OF STRONGLY PSEUDOCONVEX DOMAINS IN ALMOST COMPLEX MANIFOLDS

Abstract

In contrast with the integrable case there exist infinitely many non-integrable homogenous almost complex manifolds which are strongly pseudo-convex at each boundary point. All such manifolds are equivalent to the Siegel half space endowed with some linear almost complex structure. We prove that there is no relatively compact strongly pseudoconvex representation of these manifolds. Finally we study the upper semi-continuity of the automorphism group of some hyperbolic strongly pseudoconvex almost complex manifolds under deformation of the structure.